Central Nervous System Action on Rolling Balance Board Robust Stabilization: Computer Algebra and MID-Based Feedback Design

Using the computer algebra system Maple, we consider the stabilization of a rolling balance board by means of the multiplicity-induced-dominancy (MID) property. The human stance on a rolling balance board is analyzed in the sagittal plane through a 2-degree-of-freedom mechanical model. Namely, the human body is modeled by a double-inverted pendulum which connects to the balance board through the ankle joint. The system is stabilized by the ankle torque managed by the central nervous system (CNS). The action of the CNS is modeled by a delayed full state feedback: A pointwise delay stands for all latencies in the neuromechanical system (reaction time, neuromechanical lag, etc.). The aim of the chapter is to achieve a good occurrence in terms of the decay rate, and it exhibits the links between multiple spectral values satisfying the MID property and the exponential stability property of the solution (Note that a preliminary version of this work was published in Benarab et al. (Rolling balance board robust stabilization: A MID-based design, in TDS 2022 - 17th IFAC Workshop on Time Delay Systems, Montreal, 2022).). © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.